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Method for the Inverse Problem Solution for Reconstruction of Stress Strain State of Rock Mass Based on Natural Fractures Data

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Abstract

The paper is devoted to the problem of reconstructing stress state of the rock mass using data on natural fractures. A particular problem of reconstructing stress profiles along the well trajectory from data on spatial orientations and activity of natural fractures in well surrounding rock masses is considered. An approach for estimation of tectonic stresses from these data developed in the previous studies is considered with regard to the specifics of inverse problem solution. An optimization problem emerging during stress reconstruction procedure is stated and various methods of its solution are analyzed. Four different ways to define the objective functions measuring the degree of agreement between real and modeled fractures properties which can be used to reconstruct stresses based on natural fractures related data. The effect of objective function definition on the inverse problem solution is studied in a comparative way. To do that, a synthetic fracture model is constructed; the problem of rock mass stress state reconstruction is stated and solved for the synthetic model using different objective functions. It is revealed that variation of objective function used in practice for stress state reconstruction from natural fractures data leads both to alteration of the obtained solution for the inverse problem and solution uniqueness and stability with regard to worsening of the input data. The paper presents certain conclusions related to the suggestions on choosing a particular objective function for inverse problem solution depending on presence and quality of data related to natural fractures.

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ACKNOWLEDGMENTS

The authors are grateful to the anonymous reviewer who provided the valuable comments that led to considerable increase in quality of the paper.

Funding

The research was performed as part of the State assignment of Schmidt Institute of Physics of the Earth RAS.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Russia

    N. V. Dubinya & S. A. Tikhotskiy

  2. Schmidt Institute of Physics of the Earh RAS, Moscow, Russia

    N. V. Dubinya & S. A. Tikhotskiy

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Correspondence to N. V. Dubinya or S. A. Tikhotskiy.

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Dubinya, N.V., Tikhotskiy, S.A. Method for the Inverse Problem Solution for Reconstruction of Stress Strain State of Rock Mass Based on Natural Fractures Data. Izv., Phys. Solid Earth 58, 544–561 (2022). https://doi.org/10.1134/S1069351322040024

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